Looking to see if Blender is a good tool for an AI project
In my mind, blender is a good fit for this sort of project. It has access to python allowing high level development and the use of many many libraries. 


  What I want to know is, does the Blender game engine/python library give access to a camera 


Yes - you can extract the pixels from a camera using the ImageRender refresh() method by passing in a buffer and pixel format. I have used this for a variety of purposes in the past, though not for robotics.
https://docs.blender.org/api/blender_python_api_2_78a_release/bge.texture.html#bge.texture.ImageRender.refresh


  and stream its input in real time,


You'd have to set something up


  and is it possible to send motor sequences to a virtual arm? 


Yes. I wrote a minimal test scaffold for a UR5 robot arm. This allowed me to test a program intended for the actual hardware without needing the actual arm present. This was a huge help when trying to do a university project with limited lab time. I also somewhat sidestepped the project (with permission) by writing a blender script to generate the proper commands from the virtual setup....


  just having access to the pixel buffer is enough using, more over a high resolution isn't required, 1024x768 is plenty.


That should be possible - although you may find the GPU->CPU bottleneck on some hardware.



Some other things I have done with AI and blender include:


Testing IK solutions. 
GUI's to display telemetry and provide control of various chassis, 
Prototype control algorithms for hardware (eg four wheel omni-steer chassis - how do you co-ordinate the wheels?)
Robot hardware design - doing in in blender+BGE allows it to be tested inside the game engine before building it.